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An advertising executive claims that there is a difference in the mean household income for credit cardholders of Visa Gold and

Maslowich

Answer:

Null hypothesis: $\mu_{Visa}=\mu_{Mastercard}$

Alternative hypothesis: $\mu_{Visa} \neq \mu_{Mastercard}$

$t=\frac{66970-59060}{\sqrt{\frac{9500^2}{11}+\frac{10000^2}{17}}}}=2.108$

$p_v =2*P(t_{26}>2.108)=0.0448$

Comparing the p value with the significance level given $\alpha=0.1$ we see that $p_v$ so we can conclude that we can reject the null hypothesis, and a would be a significant difference between the in the mean household income for credit cardholders of Visa Gold and of MasterCard Gold at 10% of significance .

Step-by-step explanation:

Data given and notation

$\bar X_{Visa}=66970$ represent the mean for Visa

$\bar X_{Mastercard}=59060$ represent the mean for the sample Mastercard

$s_{Visa}=9500$ represent the population standard deviation for Visa

$s_{Mastercard}=10000$ represent the population standard deviation for Mastercard

$n_{Visa}=11$ sample size for the group Visa

$n_{Mastercard}=17$ sample size for the group Mastercard

t would represent the statistic (variable of interest)

$\alpha=0.1$ significance level provided

Develop the null and alternative hypotheses for this study?

We need to conduct a hypothesis in order to check if the means for the two groups are different, the system of hypothesis would be:

Null hypothesis: $\mu_{Visa}=\mu_{Mastercard}$

Alternative hypothesis: $\mu_{Visa} \neq \mu_{Mastercard}$

Since we don't know the population deviations for each group, for this case is better apply a t test to compare means, and the statistic is given by:

$z=\frac{\bar X_{Visa}-\bar X_{Masterdcard}}{\sqrt{\frac{s^2_{Visa}}{n_{Visa}}+\frac{s^2_{Mastercard}}{n_{Mastercard}}}}$ (1)

t-test: Is used to compare group means. Is one of the most common tests and is used to determine whether the means of two groups are equal to each other.

Calculate the value of the test statistic for this hypothesis testing.

Since we have all the values we can replace in formula (1) like this:

$t=\frac{66970-59060}{\sqrt{\frac{9500^2}{11}+\frac{10000^2}{17}}}}=2.108$

What is the p-value for this hypothesis test?

First we need to calculate the degrees of freedom given by:

$df= n_{Visa}+n_{Mastercard}-2 = 11+17-2= 26$

Since is a bilateral test the p value would be:

$p_v =2*P(t_{26}>2.108)=0.0448$

Based on the p-value, what is your conclusion?

Comparing the p value with the significance level given $\alpha=0.1$ we see that $p_v$ so we can conclude that we can reject the null hypothesis, and a would be a significant difference between the in the mean household income for credit cardholders of Visa Gold and of MasterCard Gold at 10% of significance .

4 0

3 years ago

A number that is a multiple of 2 is also a multiple of 4.If a number is a multiple of 2, then it a multiple of 4. False If a num

valentina_108 [34]

Answer:

If a number is a multiple of 2, it may NOT be a multiple of 4. An example would be the number 6.

$6\div2=3$ , but $6\div4=1.5$ .

However, if a number is multiple of 4, it is guaranteed to be a multiple of 2, since 4 itself is a multiple of 2.

Example:

$8\div4=2$

This is simply

$8\div2\div2=2$ .

It is a multiple of 2 twice.

6 0

3 years ago

Read 2 more answers

Which of the following is NOT possible? A = A triangle where one angle measures 20 degrees and another angle measures 45 degrees

ArbitrLikvidat [17]

Answer:

C

Step-by-step explanation:

the angle measures of triangles must add up to 180 degrees. Since we are only given two angles, we can assume that all of the answers that add up to be below 180 degrees fulfill this requirement with the third angle. However, answer choice C adds up to 190 degrees on the first two angle, which means that no matter how low the third angle is, it will never add up to 180 degrees.

5 0

3 years ago

What is the reciprocal of 159?

wariber [46]

<h2>Hey there! </h2>

<h2>The Reciprocal of 159 is:</h2>

$\frac{1}{159}$

${where \: 1 \: is \: hidden}$

5 0

3 years ago

A line has a slope of zero and passes through the point (-2, 3). Which of the following points must also lie on the line?

brilliants [131]

Answer:

(5,3)

Step-by-step explanation

Because the slope is 0, it means its a horizontal line. because the horizontal is on 3, then it doesnt matter what x is as long as y is 3 if that makes any sense.

7 0

3 years ago